The minute hand and hour hand form a right angle at 3:00. How long after till they form a right angle again? Give the answer to the nearest second.
let the 12 position be $\displaystyle \theta = 0$
$\displaystyle t$ = time in seconds after 3 o'clock
position of the minute hand ...
$\displaystyle \theta_m = \frac{1}{10} \frac{deg}{sec} \cdot t$
hour hand ...
$\displaystyle \theta_h = 90 + \frac{1}{120} \frac{deg}{sec} \cdot t$
the next time they are 90 degrees apart, the minute hand will have passes the hour hand ...
$\displaystyle 90 = \frac{1}{10} \cdot t - \left(90 + \frac{1}{120} \cdot t \right)$
solve for t in seconds